Master’s thesis Pseudorapidity Dependence of Elliptic Flow in Pb+Pb Collisions at √s = 2.76 TeV with ALICE NN Alexander Colliander Hansen Academic Advisor: Jens Jørgen Gaardhøje Niels Bohr Institute University of Copenhagen August 2011 English Summary This thesis presents an analysis of data from Pb+Pb collisions at a centre of mass energy of 2.76 TeV per nucleon, with ALICE at the LHC. I utilize for Forward Multiplicity Detector (FMD) and the Silicon Pixel Detector (SPD). Together the provide a pseudorapidity, η, coverage from -3.75 to 5. An analysis of the elliptic flow coefficient, v , is presented. At earlier experiments v has 2 2 been measured and found to be significant. It is interpreted as one of the most important signs of a Quark-Gluon plasma having formed in the collisions. Typically elliptic flow measurements are done as a function of the transverse momentum or centrality. Here the wide pseudorapidity coverage of the two detectors is utilized to study flow as a function of pseudorapidity. In the thesis the basic theory of high energy heavy ion physics is touched upon, with a particular focus on flow and fluctuations. The experimental apparatus is described. And a more technical description on how the detectors measure particles is presented. It is shown that most of the particles traversing the FMD is secondary particles, created in interactions with detector material. It turns out that the secondaries bias the measurements, and that a Monte Carlo correction is needed. To measure v a new method developed by people in the ALICE FLOW group is used. It 2 turns out this method is biased under certain fluctuations, which means a study of how this affects the measurement is needed. This study is done, and the optimal measuring region is found, such that unnecessary bias from fluctuations is avoided. It turns out the analysis has some problems, in particular in the FMD. A measurement is still possible, and even though it has some relatively large systematic errors, it yields a good indication on how the elliptic flow behaves as a function of η at LHC energy. The result is compared to earlier experiments at lower energies, and it is found that the shape of v (η) has changed significantly. 2 iii Resume p˚a dansk - Pseudorapiditets afhængighed af elliptisk flow i bly-bly kollisioner ved 2.76 TeV med ALICE I dette speciale præsenterer jeg en analyse af data fra bly kollisioner ved en energi p˚a 2.76 TeV per nukleon, taget med ALICE experimentet ved LHC. Jeg benytter mig af de to detektorer, Forward Multiplicity Detector (FMD) og Silicon Pixel Detector (SPD). Tilsammen dækker de et pseduorapiditets interval fra -3.75 til 5. Jeg præsenterer en analyse af den elliptiske flow koefficient, v . Ved tidligere eksperimenter 2 er v blevet m˚alt til at have en betydelig størrelse, og det anses for at være en af de vigtige 2 tegn p˚a at en kvark gluon plasma er dannet i kollisionerne. Typisk m˚ales det elliptiske flow som en funktion af den transverse impuls, eller centralitet. I denne analyse udnyttes den brede pseudorapiditets, η dækning af FMD’en og SPD’en til at kigge p˚a elliptisk flow som funktion af pseudorapiditet. Undervejs præsenteres de grundliggende antagelser i den moderne høj energi tung-ions fysik, med et specielt fokus p˚a flow of fluktuationer. Det eksperimentelle apparatur beskrives og en teknisk beskrivelse af hvordan detektorerne m˚aler partiklerne gives. Det bliver vist at størstedelen af de partikler, som rammer FMD’en er blevet skabt efter kollisionen, ved interak- tioner med forskelligt materiale i eksperimentet. Det viser sig at disse partikler er med til at forstyrre flow m˚alingen, og en korrektion baseret p˚a Monte Carlo studier er nødvendig. Til at m˚ale v koefficienten benyttes en ny metode udviklet af medlemmer af ALICE FLOW 2 gruppen. Detblivervistatdennemetodereagererspecieltp˚afluktuationer,hvilketbetyderaten kort undersøgelse af fluktuationerne indflydelse er nødvendig. Denne udføres, og det optimale m˚ale interval bestemmes, hvormed man undg˚ar unødig bias fra fluktuationer. Det viser sig at analysen har nogle problemer. En foreløbig m˚aling er dog mulig, og selvom relativt store usikkerheder præger resultaterne giver de en god indikation af hvordan det elliptiske flow som funktionafη serudvedLHCenergier. Detteresultatsammenlignesmedtidligereeksperimenter ved lavere energier, og det viser sig at formen af v (η) her ændret sig markant. 2 iv Preface In November 2009 the Large Hadron Collider at CERN collided two proton beams for the first time. Since then machine development and understanding has progressed fast, and in November 2010 the accelerator provided the LHC experiments with the first data from Pb+Pb collisions, at a centre of mass energy of √s = 2.76 TeV. The four experiments (ALICE, ATLAS, CMS NN and LHCb) have already published a number of exciting new results. With more than 2.5 fb 1 − of pp data at √s = 7 TeV delivered for both ATLAS and CMS, the two experiments are closer thanevertoeitherfindingorexcludingtheelusiveHiggsparticle. Meanwhiletheheavyiondata is being analysed and, in particular in ALICE, new heavy ion publications are coming out fast. This thesis summarises my work over the past year as a Master’s student in the High Energy Heavy Ion (HEHI) group at the Niels Bohr Institute (NBI). The work presented here is an analysis of the 2010 Pb+Pb data taken with the Forward Multiplicity Detector (FMD), which is built by the HEHI group, and the Silicon Pixel Detector (SPD) in ALICE. Using these two detectors, it is possible to measure the elliptic flow coefficient, v , over a wide pseudorapidity1 2 range, η. Flow coefficients are a Fourier expansion of the azimuthal particle yield, and the elliptic flow coefficient is the second order term (cos2φ). This term gives information on the elliptic eccentricity of the initial fireball, created in the heavy ion collision. The observation of a large elliptic flow component at earlier heavy ion experiments has been one of the strongest signals of a Quark-Gluon Plasma having formed[1]. Preliminary results from ATLAS and CMS shows v (η) in the region 2.5 < η < 2.5, the analysis presented here expands the region to 2 − 3.75 < η < 5. − The thesis is organised in the following way: Chapters 1 and 2 touches on the theoretical foundation of heavy ion physics, where Chapter 2 focus on flow and fluctuations. It is the purpose of these chapters to motivate the measurement presented in later chapters. Chapter 3 and 4 describes the experimental setup, the basics on how the detectors work and how the data is read out and processed from the detector electronics. Chapter 5 describes the method used for the flow measurement. Chapter 6 describes the analysis, and the studies carried out in order to understand the method and detectors involved. Finally in Chapter 7 the systematic errors are discussed, and in Chapter 8 it all comes together and the results are presented. Please note that the results presented here are a work in progress. They have not been approved by the ALICE collaboration yet, and should not be cited. Acknowledgements I would like to thank the High Energy Heavy Ion group at the Niels Bohr Institute (NBI), and in particular my supervisor Professor Jens Jørgen Gaardhøje for introducing me to the field of heavy ion physics, and giving me the opportunity to do this project for my Master’s thesis. Special thanks goes to Professor Jamie Nagle, who was a visiting fellow at the Discovery Center at NBI for six months, for his impressive insight in all aspects of heavy ion physics. Without his assistance and ideas I seriously doubt the analysis would have been in the almost finished state presented here, at this time. 1The pseudorapidity is a measure of the polar angle in the experiment. v I would like to thank the three PhD students in HEHI, Hans Hjernsing Dalsgaard, Casper Nygaard and Carsten Søgaard for many discussions and much help over the past year. I would like to thank Christian Holm Christensen and Hans Hjernsing Dalsgaard for the FMD and SPD codeusedtogetthedatafromESDfilestoAODfiles. AndspecialtoChristianHolmChristensen and Børge Svane Niels for proof reading this thesis and giving lots of constructive criticism. Special thanks also goes to Ante Bilandzic, whose many emails about using flow cumulants helped me understand what I was doing, and helped solve many problems encountered during the past year. I would also like to thank the FLOW group in ALICE for valuable input, the ALICE Col- laboration for providing the data, and the LHC accelerator for many days of stable beam time. Users of the coffee machine in the Q-building kitchen and Ian Gardner Bearden also deserves thanks for many encouraging words and fun breaks from the everyday thesis work. Finally, I would like to thank my family and friends; especially Ida Margrethe Ringgaard, for their love, understanding and support during the past year. With the startup of the LHC it is an exciting time to be a young student in the world of physics, and I have thoroughly enjoyed the last year at NBI and CERN. Alexander Colliander Hansen Copenhagen, August 2011 vi Contents 1 Heavy Ion Physics 1 1.1 The Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Quark-Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Heavy Ion Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 The Geometry of a Collision . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Multiplicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Transverse Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.2 High p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 t 1.5 Jet Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Flow 15 2.1 Fourier Series Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Anisotropic Azimuthal Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Azimuthal Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Higher Order Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Elliptic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5.1 p Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 t 2.5.2 η Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5.3 Model Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.6 Flow Fluctuations and Non-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 Experiment 31 3.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.1 The Four Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 ALICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 The V0 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.4 The Forward Multiplicity Detector and the Silicon Pixel Detector . . . . . . . . . 35 3.4.1 Energy Loss of Particles Traversing a Material . . . . . . . . . . . . . . . 35 3.4.2 Silicon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.3 The Forward Multiplicity Detector . . . . . . . . . . . . . . . . . . . . . . 37 3.4.4 The Silicon Pixel Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 Data 39 4.1 FMD Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2 SPD Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3 Monte Carlo Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3.1 HIJING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3.2 AMPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 vii CONTENTS 4.3.3 GEANT3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3.4 Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4.1 Reconstructing Bare Multiplicity with the FMD . . . . . . . . . . . . . . 44 4.4.2 Cluster Finding and Tracking with the SPD . . . . . . . . . . . . . . . . . 45 4.5 The Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5 Method 47 5.1 The Event Plane Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.2 Particle Cumulants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2.1 Reference Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2.2 Differential flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.2.3 Discussion On Statistical Uncertainties . . . . . . . . . . . . . . . . . . . . 54 5.2.4 Discussion On Fluctuations and Non-flow . . . . . . . . . . . . . . . . . . 55 5.3 Other methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6 Analysis 57 6.1 Resolution effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2 Toy Monte Carlo Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.2.1 No Flow Fluctuations or Non-flow . . . . . . . . . . . . . . . . . . . . . . 58 6.2.2 With Flow Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.2.3 With Non-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.2.4 With Non-uniform Azimuthal Acceptance . . . . . . . . . . . . . . . . . . 65 6.3 Discussion On Statistical Uncertainty Calculations . . . . . . . . . . . . . . . . . 65 6.4 Analysis Object Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.4.1 The SPD: From Event Summary Data to Analysis Object Data . . . . . . 68 6.4.2 The FMD: Sharing Correction With Hit Merging . . . . . . . . . . . . . . 68 6.4.3 The FMD: Particle Counting With Energy Distributions . . . . . . . . . . 71 6.4.4 The FMD and SPD: Secondary Particles . . . . . . . . . . . . . . . . . . . 76 6.4.5 The FMD and SPD: Acceptance Issues . . . . . . . . . . . . . . . . . . . 80 6.5 Full Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.5.1 Flow with an Afterburner . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.5.2 Flow with AMPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.5.3 No Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.6 Track Reference Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.7 Analysis of Real Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7 Systematic Error Estimates 93 7.1 Error Contribution From Hit Merging and Particle Counting . . . . . . . . . . . 93 7.2 Errors from the MC Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.2.1 p Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 t 7.2.2 η Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 7.2.3 Centrality Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 7.2.4 Particle ID Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 7.2.5 Material Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.3 Final Error Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 8 Results 101 8.1 Applying the Monte Carlo Correction . . . . . . . . . . . . . . . . . . . . . . . . 101 8.2 Comparing to Published LHC Data . . . . . . . . . . . . . . . . . . . . . . . . . . 102 8.3 Comparing to Previous Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 110 viii CONTENTS 9 Conclusion 115 Bibliography 117 Appendices A Statistical Uncertainties 123 A.1 Two-particle Reference Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 A.2 Four-particle Reference Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 A.3 Two-particle Differential Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 A.4 Four-particle Differential Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 B Flow Fluctuations 127 B.1 v 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 { } B.2 v 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 { } C Differential Flow Fluctuations 129 C.1 v and v are independent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 (cid:48) C.2 v and v are identical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 (cid:48) C.3 v and v are dependent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 (cid:48) D Azimuthal Coverage for Different Vertex Bins 133 E Run Number List 137 ix CONTENTS x